Ogni modulo equivale a 3 crediti ECTS. È possibile scegliere un totale di 10 moduli/30 ECTS nelle seguenti categorie:
- 12-15 crediti ECTS in moduli tecnico-scientifici (TSM)
I moduli TSM trasmettono competenze tecniche specifiche del profilo e si integrano ai moduli di approfondimento decentralizzati. - 9-12 crediti ECTS in basi teoriche ampliate (FTP)
I moduli FTP trattano principalmente basi teoriche come la matematica, la fisica, la teoria dell’informazione, la chimica ecc. I moduli ampliano la competenza scientifica dello studente e contribuiscono a creare un importante sinergia tra i concetti astratti e l’applicazione fondamentale per l’innovazione - 6-9 crediti ECTS in moduli di contesto (CM)
I moduli CM trasmettono competenze supplementari in settori quali gestione delle tecnologie, economia aziendale, comunicazione, gestione dei progetti, diritto dei brevetti, diritto contrattuale ecc.
La descrizione del modulo (scarica il pdf)riporta le informazioni linguistiche per ogni modulo, suddivise nelle seguenti categorie:
- Insegnamento
- Documentazione
- Esame
Bayesian statistics provides an alternative viewpoint to the classical ‘frequentist’ statistics by using a different, more subjective interpretation of probability. This brings various advantages in solving typical industry problems, such as the inclusion of prior knowledge, more intuitive hypothesis tests or modeling uncertainty given small amounts of data. With increasing computational power, the popularity of Bayesian statistics and machine learning has grown significantly over the past decade. This course provides students with a solid understanding of the fundamental concepts of Bayesian statistics, introduces various computational methods required in Bayesian statistics and Bayesian machine learning, and discusses numerous examples and applications of Bayesian machine learning. Bayesian as well as Gaussian process regression models are introduced and explored, with a particular focus on graphical models and Bayesian networks to model relationships and to infer causality. In addition, advanced topics and their applications are covered, such as Bayesian optimisation, non-parametric mixture models for clustering, and Bayesian neural networks.
Requisiti
Basic probability and statistics, basic programming skills (R and/or Python), linear algebra and multivariate calculus, basic concepts of machine learning.
Obiettivi di apprendimento
Students are able to formulate their problem setting on the basis of Bayesian models and to include their prior understanding. They are able to explain how Bayesian models balance between prior understanding and data towards a posterior understanding of a problem. They are aware of the advantages and disadvantages of the Bayesian approach and know in which situation it is better suited than standard frequency statistics. Since Bayesian models can rarely be computed in closed form, they are experienced in approximating posterior distributions by means of sampling-based approaches
Categoria modulo
Fundamental concepts of Bayesian statistics: Reasoning under uncertainty, probability theory, Bayes theorem, prior, likelihood, posterior, conjugate families (beta-binomial, gamma-poisson, normal-normal), sequential learning, inference, prediction
Sampling methods: Markov chains, Metropolis algorithm, Gibbs sampling, Hamiltonian MC, sequential MC
Bayesian and Gaussian Process regression: kernels, model selection, state-space models, variational inference
Bayesian networks: graphical models, causality
Selection of advanced topics: Bayesian optimisation, Bayesian non-parametric mixture modeling, Bayesian neural networks, physics-informed ML models
Metodologie di insegnamento e apprendimento
Lecture and practical work on computer.
Bibliografia
Lecture notes and notebooks will be available in addition to recommended book chapters.
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